Converts a number to base pi, demonstrating its uselessness for most numbers, example usage at top of file.

base_pi.py

#!/usr/bin/env python3

"""
	Command line use:

		$ python3 base_pi.py -3 -1 0 2 3.141592653589793238462643383279502 -9.8696044010893586188344909998761511353136 4 0.5 0.333333333333333333333
		-3
		-1
		0
		2
		10
		-100
		10.220122021121110301
		0.11211202102012230001
		0.1001111101020123002

		$ python3 base_pi.py 10
		100.01022122221121122001

	Python use:

		>>> base_pi(7)
		'20.20211200210000003002'

		>>> base_pi(-math.pi, trailing_zeroes=True)
		'-10.00000000000000000000'

		>>> base_pi(0.1, precision=40)
		'0.00300301012122112202211222000010211123'
"""


import math
import sys

# Should be enough
math.pi = 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744

def base_pi(x, precision=20, trailing_zeroes=False):
	# Assure input is valid
	x = float(x)
	precision = int(precision)
	assert(precision >= 0)
	trailing_zeroes = bool(trailing_zeroes)

	# Compute sign and make x positive
	sign = ""
	if (x<0):
		sign = "-"
		x = -x

	# Compute digits to left of point
	left_digits = ""

	if (x < 1):
		# Numbers smaller than 1 should be 0.something
		left_digits = "0"
	else:
		# Calculate the starting position
		pos = int(math.log(x, math.pi))

		# For each position [floor(log_pi(x)), ..., 1, 0]
		while (pos >= 0):
			# What digit goes in this position
			digit = int(x/(math.pi**pos))

			# Update x
			x -= digit*(math.pi**pos)

			# Update the left digits
			left_digits += str(digit)

			# Decrement pos to move right
			pos -= 1

	# Compute digits to right of point
	right_digits = ""

	# For each position [-1, -2, ..., -precision]
	for pos in range(-1,-precision-1,-1):
		# What digit goes in this position
		digit = int(x/(math.pi**pos))

		# Update x
		x -= digit*(math.pi**pos)

		# Update the right digits
		right_digits += str(digit)

	# Trim trailing zeroes
	if not trailing_zeroes:
		while len(right_digits) > 0:
			if right_digits == '0':
				right_digits = ''
				break
			if right_digits[-1] == '0':
				right_digits = right_digits[:-1]
			else:
				break

	# Format output
	if (right_digits):
		return sign+left_digits+"."+right_digits
	else:
		return sign+left_digits

if __name__ == "__main__" and len(sys.argv)>1:
	for i in sys.argv[1:]:
		print(base_pi(i))